Wells Fargo & Co. and J.P. Morgan Chase & Co., two large banks with big venture-capital arms, said their earnings will suffer in the months ahead because of weakness in the venture-capital business.

Wells Fargo, of San Francisco, said it will record expenses totaling $1.13 billion, or 65 cents a share in the second quarter, primarily because it is writing down the value of its venture-capital holdings. That would nearly wipe...